Rewrite as a simplified fraction. ${2.8\overline{1} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 281.1111...\\ 10x &= 28.1111...\end{align*}}$ Subtracting the two equations, we have: ${90x = 253}$ ${x = \dfrac{253}{90}} \text{or} {2 \dfrac{73}{90}}$